8 research outputs found
Long-term perturbations due to a disturbing body in elliptic inclined orbit
In the current study, a double-averaged analytical model including the action
of the perturbing body's inclination is developed to study third-body
perturbations. The disturbing function is expanded in the form of Legendre
polynomials truncated up to the second-order term, and then is averaged over
the periods of the spacecraft and the perturbing body. The efficiency of the
double-averaged algorithm is verified with the full elliptic restricted
three-body model. Comparisons with the previous study for a lunar satellite
perturbed by Earth are presented to measure the effect of the perturbing body's
inclination, and illustrate that the lunar obliquity with the value 6.68\degree
is important for the mean motion of a lunar satellite. The application to the
Mars-Sun system is shown to prove the validity of the double-averaged model. It
can be seen that the algorithm is effective to predict the long-term behavior
of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged
model presented in this paper is also applicable to other celestial systems.Comment: 28 pages, 6 figure
Discrete-State Abstractions of Nonlinear Systems Using Multi-resolution Quantizer
Abstract. This paper proposes a design method for discrete abstrac-tions of nonlinear systems using multi-resolution quantizer, which is ca-pable of handling state dependent approximation precision requirements. To this aim, we extend the notion of quantizer embedding, which has been proposed by the authors ’ previous works as a transformation from continuous-state systems to discrete-state systems, to a multi-resolution setting. Then, we propose a computational method that analyzes how a locally generated quantization error is propagated through the state space. Based on this method, we present an algorithm that generates a multi-resolution quantizer with a specified error precision by finite refine-ments. Discrete abstractions produced by the proposed method exhibit non-uniform distribution of discrete states and inputs.